Finite Group DatabasebetaFinite Group Databasebeta| order | 28395 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #19150943⋊C5 |
| derived, Sylow | C631 ⋊ C5×C9 |
| Hall | #19150943 ⋊ C5 |
| Hall | C631⋊C5 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C631⋊C3)⋊C5 |
| commutator, hypocenter | C631 | C5×C9 |
| Fitting, socle, cosocle | C3×C631 | C3×C5 |
| prime radical | C3×C631⋊C5 | C3 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5679 |
Polycyclic presentation:
3,5,631,3|a^3=d,c^a=c^587,c^b=c^242171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28395, 2);